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Theses and Dissertations 1. Thesis and Dissertation Collection, all items 


1987 


Models for conducting economic analysis of 
alternative fuel vehicles. 


Grenier, Danny R. 


http://ndl.handle.net/10945/22371 


This publication is a work of the U.S. Government as defined in Title 17, United 
States Code, Section 101. Copyright protection is not available for this work in the 
United States. 


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THESIS 


MODELS CR CONDUCTING ECONOMIC ANALYSIS 
OF Afar ESP Uri aC 


by 
Danny R. Grenier 


June 1987 


Thesis Advisor: Dan C. Boger 





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MODELS FOR CONDUCTING ECONOMIC ANALYSIS OF ALTERNATIVE FUEL VEHICLES 





‘2 PERSONAL AUTHOR(S) 
aC Nanny R 


"3g TYPE OF REPORT . 135 TIME COVEREO 14 OF PORT (Year Month Day) 1S PAGE COLNT 
Master's Thesis FROM TO 19875 June d 74 


"6 SUPPLEMENTARY NOTATION 





GOSATILGODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by biock number) 


FELD Aleernaeivecenuecls- se llectriec Vehicles; 
a ae Dual Fuel Vehicles; CNG Vehicles 
a 


"9 ABSTRACT (Continue on reverse if necessary and identify by block number) 
The present status of alternative fuel vehicles, specifically electric- 


powered and compressed natural gas-powered vehicles is summarized. Spee Time 
advantages and disadvantages of each vehicle type, in comparison to the 
gasoline-powered vehicle, are reviewed. A life cycle cost model is formu- 
lated for each vehicle type. An integer linear program is derived and 
explained as a means of determining the optimal mix of vehicles for a 
command's transportation fleet. The models are tested by running several 
test cases using data from the Naval Postgraduate School transportation 


office. 





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1 


Approved for public release; distribution is unlimited 


Models for Conducting Economic Analysis of 
Alternative Fuel Vehicles 


by 


Danny R. Grenier 
Lieutenant, Supply Corps, United States Navy 
B.S., Radford College, 377 


Submitted in partial fulfillment of the 
requirements for the degree of 


MASTER OF SCIENCE IN MANAGEMENT 


from the 


NAVAL POSTGRADUATE SCHOOL 
June 1987 


CC 


ABSTRACT 


The present status of alternative fuel vehicles, 
specifically electric-powered and compressed natural gas- 
powered vehicles is summarized. Specific advantages and 
disadvantages of each vehicle type, in comparison to the 
gasoline-powered vehicle, are reviewed. A life cycle cost 
model is formulated for each vehicle type. An integer 
linear program is derived and explained as a means of 
determining the optimal mix of vehicles for a command's 
transportation fleet. The models are tested by running 
several test cases using data from the Naval Postgraduate 


School transportation office. 


dels 


TABBED Or CONTENTS 





INTRODUCTION ------------------------ +--+ 
A. PROBLEM STATEMENT ----------------------~~~~~ ~ 
B. OBJECTIVE --------------------------~ 
Cc: ALTERNATIVES ----------------~----- +--+ 
D. ALTERNATIVE SELECTION CRITERIA —-———— == 
E. MEASURES OF EFFECTIVENESS —————_ =e 
F. ASSUMPTIONS -------------------------~-+- 
G. RESEARCH METHODS ----------------------~~~~ — 
H. SUMMARY ----------------------------~ 
ALTERNATIVES ---------------------- — + 
A. ELECTRIC=-POWERED VEHICLES ---------------~~-—— 
1. Background ------------------- ---------+-- 
2. Vehicle Description --------------------- 
a. The Battery ------------------------- 
b. The Controller =-—--====—-=.=.-—]]-]2.. 22 
Ss The Motor --------------------~---~~-~-~-— 
d. The Transmission -<-<----------<------— 
e. The Differential -------------------~- 
3. Advantages of Electric-Powered Vehicles - 
4. Disadvantages of Electric-Powered 
Vehicles --------------------------~+~-~-~~ 
5. Electric-Powered Vehicle Performance 
Data ----------------- - - - - - - - - - - 
6. Electric-Powered Vehicle Cost Data ------ 


11 


12 


i2 


Te 


16 


Ls 


18 


18 


20 


20 


23 


24 


24 


25 


25 


26 


26 


28 


mil. THE 


IV. THE 


APPENDIX: 


COMPRESSED NATURAL GAS-POWERED VEHICLES ----- 
1. Background ----------------9 999-52 ------- 
2. Vehicle Description --------------------- 


3. Advantages of Compressed Natural Gas 
Vehicles -------------------------------- 


4. Disadvantages of Compressed Natural 
Gas Vehicles ---------------------------- 


5. Compressed Natural Gas Vehicle 
Performance Data ------------------------ 


6. Compressed Natural Gas Vehicle 
Cost Data ------------------------------- 


LIFE CYCLE COST MODEL ----------------------- 
LIFE CYCLE COST COMPONENTS ------------------ 
LIFE CYCLE COST FORMULA --------------------- 
CASOMNE-—POWERED VEHICLE Etat CYCLE COST ==-- 
Preece POVERE Dev EneeCEE LiFe -CyYCchn coOsr ——-—— 


COMPRESSED NATURAL GAS-POWERED VEHICLE 
LIFE CYCLE COST ----------------------------- 


LINEAR PROGRAMMING MODEL -------------------- 
FIXED CHARGE INTEGER LINEAR PROGRAM MODEL --- 
SUMMARY AND CONCLUSIONS --------------------- 


VERCLE DLiRE CYGCERE COST €COMeEUrALIONS ==--=-=-- 


LIST OF REFERENCES errr rrr rrr tt tr strstr tert ttc ccc cccscccc 


INITIAL DISTRIBUTION LIST cerrrrrr rr rrr rrrrrrrrrssrscrc--- 


31 


SL 


33 


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36 


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44 


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a2 


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64 


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ea 


73 


ive INTRODUCETON 


Today's military managers must contend with decreasing 
budgets while mission requirements continue to expand. In 
order to meet these expanding requirements, military 
managers must conserve the scarce financial resources 
available to them. 

The Public Works Center Transportation Office is 
required to provide vehicles for the transportation 
requirements oof the commands it supports. These 
transportation requirements run the gamut from maintenance 
vehicles to passenger sedans to passenger buses. The means 
of propulsion for all of these vehicles is usually the 
internal combustion engine with gasoline as the fuel source. 

Recent history has shown the price of gasoline to be 
somewhat less than _ stable. This instability can be a 
financial manager's nightmare. Departmental budgets are 
forecasts or predictions of what funds the department 
believes it will require for some future period. In the 
government, this future period can be more than a year away. 
Thus, the budget the transportation manager submits today 
can be drastically affected by an increase in the price of 
gasoline tomorrow. What the transportation officer desires 
is a fuel source which is cost effective and stable in 


price. 


Two alternative fuel source vehicles that have generated 
interest within the transportation industry are electric- 
powered vehicles and compressed lgvstieblersi IL gas-powered 
vehicles. 

This thesis looks at these two alternative fuel vehicles 
and compares them to the present baseline of the gasoline- 
powered internal combustion engine vehicles. In order to 
Simplify matters, this thesis will only deal with sedans, 
vans, and light trucks. 

Formulas for computing the life cycle costs of the 
vehicles are derived in the thesis. After determining the 
life cycle costs of the various types of vehicles, the 
transportation manager must decide what mix of the various 
types of vehicles would allow him to meet his operational 
requirements at the lowest cost. In other words, what mix 
allows him to optimize his transportation budget? 

The thesis explains the use of a fixed charge linear 
program to obtain the optimal mix of vehicles. Linear 
programming is an operations research tool which is used to 
determine the optimal allocation of limited resources, in 
this case, the transportation budget. fieeaoing lanear 
programming, the manager can subject the results’ to 
sensitivity analysis which allows the manager to test the 
optimal solution by changing the various constraints such as 


the funding level or various cost elements (i.e., fuel cost, 


maintenance cost, operating cost) and observing the effects 


on the optimal solution. 


we PROBLEM STATEMENT 

The instability of the cost of gasoline has stimulated 
an interest in alternative fuel vehicles. A means to 
compute the life cycle costs of the various types of 
vehicles is required. Having determined the life cycle 
costs of the various vehicle types, the transportation 
manager requires a means of determining the optimal mix of 
the vehicle types based on his budget constraint and mission 


requirements. 


Bi OBUECTIVE 

The research objective is to derive a procedure for 
computing the various vehicle life cycle costs, then use 
these life cycle costs to determine the optimal mix of 
vehicle types. The underlying objectives are: 


1. Present an overview of the present state of the art of 
the electric-powered vehicle industry and the 
compressed natural gas-powered vehicle industry. This 
overview will include an assessment of the operational 
capabilities of both the electric-powered vehicle and 
the compressed natural gas-powered vehicle. 


2. Develop a model for determining the life cycle costs 
of the various vehicle types. 


3. Develop a fixed charge linear program for determining 
the optimal mix for a typical Public Works Center 
transportation fleet. 


C. ALTERNATIVES 

The - alternatives to the gasoline-powered internal 
combustion engine vehicle that are considered are the 
electric-powered vehicle and the compressed natural gas- 
powered vehicle. 

The electric-powered vehicle has been tested extensively 
by large companies and the United States Postal Service. 
While it is not a widely used vehicle in the United States, 
it is quite popular overseas. There are various limitations 
on the use of the electric vehicle due to its limited range 
and cruising speed. 

The electric vehicle must be recharged daily. A few 
models of electric vehicles are equipped with an onboard 
charging unit but this is the exception rather than the 
rule. As such, the electric vehicle is usually required to 
return to the charging unit each night. This makes the 
electric vehicle impractical for extended trips. 

Another limitation on the use of the electric vehicle is 
the cruising speed attainable by the vehicle. While some 
vehicles are able to attain speeds of over 55 miles per 
hour, this, again, is the exception rather than the rule. A 
drawback of attaining high speeds in an electric vehicle is 
that the range of the vehicle is drastically decreased with 
an increase in speed. Most electric vehicles are designed 
to operate most efficiently at speeds of up to 35 miles per 


MOUTr . 


The compressed natural gas-powered vehicle has been used 
extensively by natural gas utility companies in the United 
States. Much like the electric vehicle, it enjoys more 
popularity overseas than in the United States. The 
compressed natural gas-powered vehicle that is most popular 
is actually a conversion of the gasoline-powered internal 
combustion engine vehicle. The conversion process allows 
the vehicle to operate using either compressed natural gas 
or gasoline. Due to this ability to use two fuels, it is 
termed a dual fuel vehicle. 

Due to this dual fuel capability, the compressed natural 
gas vehicle does not have the range limitations that the 
electric vehicle carries. If a compressed natural gas 
vehicle is required to operate in an area where natural gas 
refueling equipment is not available, a simple turn of a 
valve will switch the vehicle from natural gas fuel to 
gasoline. 

The primary limitation caused by the compressed natural 
gas conversion of the gasoline internal combustion engine 
vehicle is a loss of cargo space due to installation of the 
compressed natural gas cylinders. 

The electric-powered vehicles and the compressed natural 
gas-powered vehicles will be judged against the baseline of 
the gasoline-powered internal combustion engine vehicle. 
Due to the widespread use of the gasoline vehicle and its 


operational capabilities, there are few limitations on the 


10 


vehicle type. Range is unlimited due to the many gasoline 
stations in the United States and overseas. Nearly all 
gasoline-powered vehicles can easily attain the national 
speed limit of 55 miles per hour. 

Due to the unlimited range and the high cruising speed 
attainable by gasoline-powered vehicles, these vehicles are 
considered high performance vehicles. In contrast, low 
performance vehicles would be characterized by cruising 
speeds of less than 55 miles per hour and reduced range. 

For the purpose of this thesis, the optimal vehicle is 
the vehicle which meets the minimum mission requirements 


placed upon it at the lowest life cycle cost. 


D. ALTERNATIVE SELECTION CRITERIA 
The two keys to determining the optimal vehicle for a 
particular task are: 


1. Determining the requirements that will be placed upon 
the vehicle. 


2. Determining which vehicle type can meet the minimum 
requirements of the task at the lowest life cycle 
cost. 


These two keys require the Public Works Center 
transportation officer to first determine the types of 
requirements that are placed on his vehicle fleet. These 
requirements are usually in terms of range, cruising speed, 
and load. 

Once the transportation officer has determined how many 


high performance vehicles and low performance vehicles are 


Itt 


required to meet the requirements placed on his department, 
he can then look at meeting these requirements with the 


lowest life cycle cost vehicle type. 


E. MEASURES OF EFFECTIVENESS 

The following measures of effectiveness are used to 
determine whether a vehicle type is classified as high 
performance or low performance. 


1. Range--Range is defined as the distance a vehicle can 


travel between refuelings. For the purposes of this 
thesis, the terms refueling and recharging are 
synonymous. A high performance vehicle is capable of 


unlimited range. A low performance vehicle's range is 
limited by the location of its refueling station. 
(homebase). 


2. Maximum cruising speed--The maximum cruising speed is 
defined as the maximum speed a vehicle must be able to 
attain and travel at for an extended period of time. 
This is not to be confused with the maximum speed 
attainable by a vehicle which is the highest speed a 
vehicle can attain but can't hold for an extended 
period of time without risking damage to the vehicle. 
A high performance vehicle 1s capable of attaining a 
maximum cruising speed of 55 miles per hour, the 
national speed limit. A low performance vehicle's 
maximum cruising speed is less than 55 miles per hour. 


The load capabilities of the vehicle types are more a 
function of the individual vehicle design rather than the 
vehicle type and as such load capability will not be used as 


a measure ort GlEeCCEivVeness. 


F. ASSUMPTIONS 
In order to conduct this study, certain assumptions have 
been made. Those assumptions are: 
1. The number of vehicles needed to meet the requirements 


placed upon the Public Works Center transportation 


12 


office will not change due to the type of vehicle 
chosen to meet the requirement. The number of 
vehicles in the transportation office fleet will 
remain constant. 


2. Future requirements placed upon the vehicles will be 
consistent with past requirements. Required range and 
maximum cruising speed for a particular vehicle will 
not change in the near future. 


3. Initial procurement cost, maintenance cost per mile, 
operating cost per mile, and fuel efficiency ratings 
are equal for each vehicle in a particular vehicle 
type (i.e., gasoline-powered, electric-powered, or 
natural gas-powered). 


4. All vehicles will be procured at the same time, Year 
1, and disposed of at the end of their useful life. 


5. All cost data used in the life cycle cost model will 


be in 1986 dollars. Cost figures from research 
Material will be adjusted to reflect value in 1986 
dollars. Adjustments will be made in accordance with 


Table 1, which lists the Consumer Price Indices for 
gasoline, natural gas, electricity, new automobiles, 
and the general price index of all items. 
fee RESEARCH METHODS 
A literature search was conducted to obtain a 
bibliography of articles, studies, and research papers 
written on the current state of the art of electric-powered 
vehicles and compressed natural gas-powered vehicles. The 
search included articles on the claimed performance 
capabilities of the alternative fuel vehicles as well as 
actual usSe studies done on the vehicles. These performance 
capabilities were used to classify the alternative fuel 


vehicle types as either high or low performance vehicles. 


13 


Year 


Lo ZO 
uo7 
ow Z 
L9o73 
1974 
LoS 
L376 
oa 
L378 
Low S 
1980 
19'S. 
£982 
£933 
1984 
1985 
1986 


Note: 


Sources: 


Gasoline 


105. 
106. 
107. 
ior. 
os 
oe 
ee 
Loor 
T2O. 
260. 
Oo 
410. 
369%. 
Beh Oe 
O87 O%. 
370% 
202. 


mM ON W WY O FP WwW NY OO WO OO FF HW WwW DW 


CONSUMER PRICE INDICES OR 


TABLE 1 


1970 THROUGH T9eGec 


oie7 


Natural Gas 


108. 
ioe 
22 
lez ae 
143. 
7 ee 
20u 
Zoo 
265). 
BO Sz 
363. 
414. 
497. 
580. 
584. 
556. 
B23. 


Or ££ RP NY WO HO W FP WN OH OO YO W NY WO 


100 


EVeGtt vemsee, 


106. 
Tae 
i TSe 
124. 
147. 
167. 
La 
oo 
Z0er 
Zeno 
Za36 
291. 
Bia Ol 
330% 
Soe 
BOT. 
S20 


rPmMm on ww Ww FP RP FF WH ODO MH OO WO N WN 


New 
Autos 
LOge 
i238 
a 
LL 
Lig 
2a 
13: Si 
142% 
L538 
166. 
179% 
190. 
LS7. 
2025 
2087 
219. 
234 


“I N Ol Oy Ol ® WO © © 70 =! OF OF owe 


All 
Items 
11Ge 
120 
1252 
133% 
147% 
16.8 
170 
1818 
1952 
2172 
246. 
2726 
289= 
298. 
3. 
328% 
3256 


J ff RP FP FP FP DO FP FON NN N RP WW W 


Indices cited for 1985 and 1986 are the indices as of 


U.S. 


Department of Commerce, 
of the United States, 


the end of December 1985 and December 1986. 


Statistical Abstract 
1976 and 1986. 


U.S. Department of Labor, CPI Detailed Report, 
December 1985 and 1986. 


14 


The literature provided cost data on initial procurement 
costs, maintenance costs, operating costs, and supporting 
equipment costs of the alternative fuel vehicles. 

The literature search provided points of contact for 
additional information. Telephone interviews were conducted 
with several electric vehicle manufacturers and the American 
Gas Association. As a result of these telephone interviews, 
additional research material was forwarded to the thesis 
writer. This additional information included cost and 
performance data. 

The cost data derived from the above research was used 
to compute a life cycle cost for each alternative fuel 
vehicle type. The fuel cost rates used in the life cycle 
cost determination were those rates paid by the Naval 
Postgraduate School in 1986. 

The life cycle cost of the gasoline-powered vehicle was 
derived using 1986 cost data from the Naval Postgraduate 
Sehool transportation office. Initial procurement cost, 
operating cost per mile, and maintenance cost per mile are 
the computed averages for all gasoline-powered sedans, vans, 
and light trucks in the Naval Postgraduate School vehicle 
fleet. 

If the study were to determine that an alternative fuel 
vehicle should be used in the transportation vehicle fleet, 
there would be a fixed cost of the price of the fueling 


Station. In the case of an electric-powered vehicle, the 


isd 


fueling station would be a charging unit. For a compressed 
natural gas-powered vehicle, the refueling station would be 
a natural gas compressor. Due to this fixed charge 
component in the life cycle cost, a fixed charge linear 
program was deemed appropriate for determining the optimal 
mix of vehicle types in the vehicle fleet. Constraints in 
the linear program were derived from the transportation 
office budget and the operational requirements placed upon 


the vehicle fleet. 


H. SUMMARY 

This thesis reviews the current state of the art in 
electric-powered vehicles and compressed natural gas-powered 
vehicles. A means of determining the mix of high and low 
performance vehicles required to meet mission requirements 
is submitted. A model for computing the life cycle cost of 
a vehicle type is explained and then used in a fixed charge 
linear program to determine the optimal mix of vehicles to 
meet the requirements placed upon the vehicle fleet. 

The models and linear program are tested by using the 
Naval Postgraduate School transportation office vehicle 
fleet as a test case. 

Chapter II of the thesis evaluates the advantages and 
disadvantages of each of the vehicle types. Based on the 
range and maximum cruising speeds of the vehicle types, the 
vehicles are classified as either high or low performance 


vehicles. 


16 


In Chapter III, the cost components of the life cycle 
cost model are explained and the life cycle cost model is 
formulated. The costs associated with each vehicle type are 
then put into the life cycle cost model to obtain the life 
cycle costs for each vehicle type. 

In Chapter IV, the fixed charge linear program model is 
explained. The life cycle costs computed in Chapter III are 
then put into the fixed charge linear program. The 
constraints used in the fixed charge linear program are 
based on the Naval Postgraduate School transportation 
office's mission requirements and budget. By using the 
fixed charge linear program, an optimal mix of vehicles for 


the Naval Postgraduate School vehicle fleet is determined. 


Le 


Ii. ALTERNATIVES 


This chapter begins with a brief description of the 
electric-powered vehicle and how it operates. Performance 
Gata derived from tests of various models of electric- 
powered vehicles will be presented for use in classifying 
the electric-powered vehicle as either high or low 
performance. Cost data concerning the electric vehicle's 
procurement cost, maintenance cost, and fuel cost will also 
be presented. 

Following the section on electric-powered vehicles, the 
compressed natural gas-powered vehicle will be described. 
Performance data will be presented as will cost data on 


procurement, maintenance, and fuel. 


As ELECTRIC—-POWERED VEHEGCEES 
1. Background 

At the beginning of the twentieth century, the 
electric vehicle was in direct competition with the gasoline 
powered vehicle. The scarcity of gasoline stations made the 
electric vehicle a viable option to the gasoline vehicle. 
However, with the rapid growth of the gasoline service 
station industry came the demise of the electric-powered 
vehicle. The demise of the electric-powered vehicle was 
attributable to its limited range and unreliable power 


source, the batteries. (Ref. l:p. 24] 


iS 


During World War II, due to gas_ shortages and 
rationing of gasoline, there were approximately 6,000 
electric-powered vehicles in operation in the United States. 
Following the war, the growth of the electric vehicle 
industry continued until it reached its highpoint in the 
1960s when there were approximately 45,000 electric vehicles 
in use in the United States. At that time, the electric 
vehicle was mainly being used for delivery service in 
industries such as the dairy industry. [Ref. l:p. 24] 

An electric-powered vehicle with a range of 40 to 50 
miles between chargings could be built with the technology 
available today. An electric vehicle with this range would 
be capable of meeting 95% of the daily driving needs of a 
typical United States car owner. [(Ref. 2:p. 1388] 

The electric vehicle manufacturing industry in the 
United States consists mainly of small manufacturing firms. 
Most of the United States electric vehicle manufacturers 
believe that the most popular and efficient electric-powered 
vehicle model is either the small passenger car or the small 
van. The body design of the vehicle is most often a 
conversion of an existing gasoline vehicle's body. (Ref. 
mepp- 629-630 ] 

Since the recent oil glut began in the early 1980s, 
many of the small electric-powered vehicle manufacturers 
have gone out of the electric vehicle production business 


citing low demand for electric vehicles. However, the 


19 


electric vehicle industry continues to grow overseas, 
especially in Great Britain. 

The largest single test program of electric-powered 
vehicles was conducted by the United States Postal Service. 
The test began in August 1971. A total of 383 electric- 
powered vehicles were used. The majority of the vehicles 
were converted AM General Jeeps. The results of the test 
will be included in the electric vehicle performance data 
section of this thesis. [Ref. 3:p. 630] 

2. Vehicle Description 

The basic electric vehicle drivetrain consists of a 
battery, a controller, a motor, a transmission, and a 
differential layed out in accordance with the following 


schematic. 


Battery---Controller---Motor---Transmission---Differentital 


The battery is the source of all the propulsion energy. The 
controller regulates the power supplied to the motor. The 
motor converts the power into rotary motion which the 
transmission matches to that of the axle. Finally, the 
differential balances the power supplied to each of the 
drive wheels. [Ref. 4:p. 20] 
a. The Battery 
The Noyes Data Corporation in their 1979 book, 


Electric and Hybrid Vehicles, states: 


Batteries represent only 10 percent of the initial 
cost of today's electric vehicle, yet the ultimate 


20 


operating costs of electric vehicles are heavily dependent 
on battery performance. The energy and power available 
from a battery directly affect the road performance of an 
electric vehicle. The cycle life and maintenance 
requirements contribute directly to the ultimate operating 
cost, and the complexity of the battery system is directly 
melated to reliabilaty. [Ref. 3:p. 347] 

The most widely used type of battery is the 
lead-acid battery similar to that used in gasoline-powered 
vehicles. While there are other types of batteries such as 
nickel-zince and nickel-iron, the lead-acid battery is the 
most popular and will be the battery on which test results 
and cost data are based. 

There are four types of lead-acid batteries. 
The starting, lighting, and ignition lead-acid battery is 


the battery used in gasoline-powered vehicles. Another type 


of lead-acid battery is the type used in most electric- 


powered golf cars. The final two types of lead-acid 
batteries are the semi-industrial and industrial. [Ref. 
3:p. 350] 


The starting, lighting, and ignition battery is 
designed to deliver high power for short periods of time. 
The golf car battery is designed to deliver high power for 
relatively long periods of time while minimizing the battery 
weight. The semi-industrial and industrial batteries are 
not so much concerned with the weight of the battery as they 
are the length of time the battery can deliver a high amount 


of power. Based on its size and low weight, the golf car 


Za 


battery is the type of lead-acid battery most used in 
electric-powered sedans and small vans. [Ref. 3:p. 350] 

The deep-discharge life cycle of a battery 
determines the useful life of a battery. For a golimieans 
battery, the deep-discharge life cycle is estimated at 200 
tom400m@eyVeles. For purposes of determining the life cycle 
cost of the electric-powered vehicle, the deep-discharge 
life of the golf car battery will be fixed at 300 cycles. 
(Ref. Siipkes 52) 

The performance of the battery is greatly 
affected by its operating environment. The battery capacity 
of a battery at 32 degrees F is only 60% of that of a 
battery at 72 degrees F. Thus, the cold weather performance 
level of an electric-powered vehicle will be much lower than 
its warm weather performance level. Range of the vehicle 
and its acceleration will be reduced due to the lower 
battery capacity. [Ref. 3:p. 358] 

The recharging of a lead-acid battery usually 
takes between four and twelve hours. Overcharging was 
batteries can lead to loss of water in the battery, 
requiring additional maintenance and its accompanying costs. 
Undercharging of the battery results in reduced range. The 
controlling of the charging of the battery is usually done 
by the battery charger. Present day chargers are not 


capable of adjusting the charging period of a battery based 


Z2 


on temperature or the age of the battery. [RereweSe Dp. 363— 


364] 
beeethe Controller 
The controller acts as the link between the 
battery and the motor. It allows the electric vehicle 


operator to control the amount of power which flows from the 
battery to the motor. The controller should provide the 
following: 
(1) Smooth operation at and near zero speed for good 
maneuverability and parking 
(2) Smooth acceleration at the operator selected rate to 
the desired speed 
(3) Operation at any operator-selected constant speed 
(4) Smooth deceleration where regenerative braking is 
employed 
(5) Efficient, safe, and reliable operation 
(6) Overload protection for motors, motor reversing, and 
charging of auxiliary batteries. [Ref. 3:p. 171] 
Since all current electric vehicles use direct 
current (DC) motors, the controller varies the voltage and 
the current to the motor in order to control the flow of 
power. feet. 3:0. 171] 

The regenerative braking mentioned in (4) above 
is a means of charging the battery through the use of the 
energy loss which occurs when the vehicle brakes. In most 
conventional vehicles friction brakes are used. The kinetic 
energy loss resulting from braking a conventional vehicle is 
lost in the form of heat. In the electric vehicle, the 
kinetic energy loss can be recovered electrically and used 


to charge the battery, thus extending the range of the 


vehicle. In regenerative braking, the electric vehicle's 


23 


motor acts as a generator sending a charge to the battery 
and a resistive load to the wheels thus braking the vehicle. 
The controller must be able to control the amount of charge 
flowing to the battery if regenerative braking is used in 
the electric vehicle. [Ref. 5:p. 149] 

c. The Motor 

The direct current (DC) motor is the most 
popular type of motor used in an electric vehicle mainly due 
to the types of demands placed on an electric vehicle. The 
DC series motor delivers a high torque per ampere ratio 
under heavy loads thus reducing the battery drain of the 
electric vehicle during acceleration or climbing hills. 
(Ret. 33). 269) 

dad. The Transmission 

If the only means of varying the motor speed and 
torque of the electric vehicle were the controller, the 
electric vehicle would be unable to operate efficiently. 
The transmission allows the electric vehicle to maximize the 
power and the efficiency of the electric motor. It provides 
better vehicle acceleration and hill climbing ability. 
[Rei. . 3: pawl6 1) 

The most common type of transmission used in 
electric-powered vehicles is the manual shift multi-gear 
transmission. The popularity of the manual transmission is 
mainly due to its size, durability, efficiency, and low 


price. sqRet 7303p. 16>) 


24 


Another popular transmission is the automatic 
shift transmission whose shift points are designed to 
Seincide with the motor'’s “characteristics. The main 
disadvantages of this type of transmission are its higher 
cost and weight, and its lower efficiency when compared to 
the manual multi-gear transmission. [Ref. 3:p. 165] 

The Continuously Variable Transmission (CVT) is 
a transmission option which is currently being developed by 
electric vehicle manufacturers. Its yet to be realized 
goals are to offer the advantages of a fully automatic 
transmission with the energy efficiency of a manual multi- 
gear transmission. [Ref. 5:pp. 176-178] 

e. The Differential 

The differential is used to equally distribute 
the load to the drive wheels when they rotate at different 
Speeds aS in cornering. The differentials used in all the 
current electric-powered vehicles are the conventional 
differential found in gasoline-powered vehicles. [Ref. 3:p. 
159] 

3. Advantages of Electric-Powered Vehicles 
The following are the claimed advantages of using an 
electric-powered vehicle. 

1. Increased Reliability. The long life and simplicity 
of electric vehicle components will lead to more 
reliability and lower probability of breaking down. 
While most tests have actually found that electric 
vehicles are no more reliable than gasoline-powered 


vehicles, some electric vehicle proponents believe 
that if production of electric vehicles were 


25 


increased, the reliability benefit would be realized. 
PRef. 4¢pee212) 


2. Low Maintenance. Scheduled and unscheduled 
maintenance will be reduced by as much as two-thirds 
of that required to be performed on gasoline-powered 
vehicles. [Ref. 4:p. 212] 


3. Less Dependence on Oil Imports. Since an electric 
vehicle does not use gasoline, an increase in the use 
of electric-powered vehicles would lower our 


requirement for oil. 


4. Less Pollution. Since electric vehicles do nowwoeuwen 
gasoline there will be less pollution. 


5. Less Noise. Electric-powered vehicles are quieter 
than gasoline-powered vehicles. [Ref. 5:p. 8] 


4. Disadvantages of Electric-Powered Vehicles 
The following are the disadvantages associated with 


using an electric-powered vehicle. 


1. Lower Performance. The range of an electric-powered 
vehicle is much lower than that of the gasoline- 
powered vehicle. The maximum cruising speed and 


acceleration rate of electric vehicles are also lower 
than those of the typical gasoline-powered vehicle. 
[Reis -42p.. 213] 

2. More Expensive. The initial procurement cost and the 
total life cycle cost of an electric vehicle is higher 
than that of a comparable size gasoline-powered 
vehicle based on current fuel and maintenance costs. 
[Ref. 4:p. 214] 

5. Electric-Powered Vehicle Performance Data 
The performance measures which will be addressed in 
this thesis are, first, range between chargings’9 and, 
secondly, maximum cruising speed. These two performance 


measures will be used to classify the electric-powered 


vehicle as either a high or low performance vehicle. 


26 


The range of the electric-powered vehicle is a 
function of the speed the vehicle is traveling and the load 
placed upon it. The environment that the vehicle operates 
in, the skill of the operator, and the vehicle's condition 
also greatly affect the range of the vehicle. 

The following test results are derived from data 
reported by Noyes Data Corporation in its book Electric and 
Hybrid Vehicles. Tests were conducted on 23 electric- 
powered vehicles ranging in size from a two-passenger 
vehicle to a van. 

1. Maximum Speed: Values ranged from 31 miles per hour 
to 56 miles per hour. The average maximum speed was 
43 miles per hour. This is well below the high 
performance parameter of 55 miles per hour maximum 
cruising speed. [Ref. 3:p. 47] 

2. Range at 25 miles per hour (constant speed): Values 
ranged from 26 miles to 117 miles. The average range 
at a constant speed of 25 miles per hour was 54 miles. 
[Rete s > Dp. .47 | 

3. Range at 35 miles per hour (constant speed): Only 11 
out of the 23 electric-powered vehicles were able to 
complete this test. The values ranged from 23 miles 


to 88 miles. The average range at a constant speed of 
35 miles per hour was 47 miles. [Ref. 3:p. 47] 


4. Range at 45 miles per hour (constant speed): Only 
five out of the 23 electric vehicles were able to 
complete this test. The values ranged from 25 miles 


to 71 miles. The average range at a constant speed of 
45 miles per hour was 38 miles. [Ref. 3:p. 47] 


Several tests were conducted to find the range of 
electric-powered vehicles under stop and go - driving 
conditions. These tests were conducted in accordance with 
schedules written by the Society of Automotive Engineers in 


SAE J227a, Electric Vehicle Test Procedure, dated February 


Pat 


1976. Each test was terminated when the test vehicle's 
acceleration was insufficient to reach the required cruising 
speed within the required time, although the vehicle could 
continue to operate. [Ref. 3:pp. 39-41] 

1. The first test simulated a fixed route in an urban 
setting. The distances traveled until the next test 
was terminated, ranged from 20 miles to 80 miles. The 
average distance was 38 miles. [Ref. 3:pp. 41,47] 

2. The second test simulated a variable route in an urban 
setting. Twelve of the 23 vehicles were able to 
complete this test. The distances traveled ranged 
from 20 miles to 77 miles. The average distance was 
36 miles. [Ref. 3:pp. 41,47] 

The second stop and go driving test will be used to 
judge overall vehicle range as it best approximates a 
typical driving environment ona Navy base or station. 

Based on the test results, the electric vehicle must 
be classified as a low performance vehicle for both maximum 
cruising speed and range reasons. The maximum cruising 
speed is, on average, 43 miles per hour with 45 miles per 
hour attainable on 5 out of 23 models tested. The range is 
limited to about 36 miles between charges. 

6. Electric-Powered Vehicle Cost Data 

The cost data this thesis will review pertains to 
initial procurement cost, fuel cost per mile of operation, 
maintenance cost per mile of operation, battery replacement 
cost, and battery charger cost. 

A 1977 survey of manufacturers of electric vehicles 


in the United States found that the initial procurement cost 


of an electric vehicle ranged from $3300 to $10,800. The 


28 


cost of the electric vehicle was found to be roughly 
proportional to its weight ($4 to $6 per kilogram). In 
comparison, a gasoline-powered vehicle costs roughly $3 per 
kilogram. This means that an electric vehicle's initial 
procurement cost is anywhere from 34% to 100% higher than 
that of a gasoline-powered vehicle. [Ref. 3:p. 93] 

In doing life cycle cost estimates of electric- 
powered vehicles for this thesis, it will be assumed that 
the initial procurement cost is 1.5 times the average cost 
of a gasoline-powered vehicle. The salvage value of the 
electric vehicle is estimated at six percent of its 
procurement cost. The salvage value is based on the scrap 
metal value of the vehicle. [Ref. 6] 

Fuel estimates for electric vehicles used by the 
United States Postal were between 1.2 and 1.5 kilowatt hours 
per mile of operation [Ref. 7:p. 739]. An electric-powered 
vehicle requires approximately 40 kWh per battery recharge 
(Ref. 5:p. 249]. Based on this refueling measure, the fuel 
cost estimate per mile of operation can be derived by: 

1. Dividing 40 kWh by the range of the electric-powered 


vehicle. Based on the earlier test range of 36 miles, 
the fuel estimate per mile of operation is: 


40 kWh 


Gear 1.11 kWh per mile 


2. Then multiply the fuel estimate per mile times the 
cost of a kWh of electricity. 


The primary maintenance cost of electric-powered 


vehicles is battery maintenance. The time required to 


29 


conduct battery maintenance is dependent on the number of 
batteries, how hard it is to get them to conduct 
maintenance, and the size of the batteries. Maintenance 
costs also depend on how the batteries are being charged. 
Overcharging leads to loss of battery fluid which requires 
more than normal maintenance. 

William Hamilton, in his article, "Costs of Electric 
Vehicles inn peocal Fleet Service," states that the 
Maintenance costs of electric-powered vehicles will be 65% 
of the current cost to maintain gasoline-powered vehicles. 
He derives this figure by determining what percent of a 
gasoline vehicle's maintenance cost is directly attributable 
to the internal combustion engine components of the vehicle. 
[REE s. 3 pp< 3759-740 | 

Further research has found no better means of 
estimating maintenance costs, therefore Mr. Hamilton's 
estimating tool of 65% will be used to figure the 
maintenance cost per mile of operation. 

The battery replacement cost for golf car type 
batteries in 1979 was $50 per kWh [Ref. 3:p. 356]. Assuming 
that the electric vehicle is using a 40 kWh battery, the 
cost of replacing the battery would be $2000 in 1979 
dollars. The life of the battery in terms of miles can be 
figured in the following manner. It was assumed earlier 
that a battery's deep cycle life was 300 cycles. The range 


of the vehicle per cycle is 36 miles. Therefore, the life 


30 


of the batteries in terms of miles is 10,800 miles, 36 miles 
per cycle x 300 cycle battery life. An experimental battery 
constructed with nickel-zinc has attained a cycle life of 
100 cycles. If the battery can be mass produced, the cost 
per kWh is estimated to be $50 in 1979 dollars. {[{Ref. 5:p. 
216] 

According to Department of Energy studies, the range 
in the cost of battery chargers for electric-powered 
vehicles was $550 to $1300 in 1986. The more expensive 
battery chargers offered options such as timers. The 
average cost of a battery charger was estimated to be $650. 
The expected life of the battery charger was 10 years with 
no annual maintenance expenses forecasted. No special power 
requirements or installation requirements accompanied the 


purchase of the battery charger. [Ref. 8] 


B. COMPRESSED NATURAL GAS-POWERED VEHICLES 
ito bAackKoOround 

The first practical natural gas power engine was 
invented by Nicholas Otto in 1976, nine years before Karl 
Benz built the first internal combustion engine-powered 
vehicle. Since those early days, compressed natural gas- 
powered vehicles have proven themselves to be ae safe 
alternative to the gasoline-powered vehicle in = many 
countries around the world. Hundreds of thousands of 
compressed natural gas-powered vehicles are currently in 


operation in countries such as Italy, China and New Zealand. 


oak 


In the United States and Canada there are approximately 
30,000 compressed natural gas-powered vehicles on the road. 
(Ref. 9:p. 46] 

One hundred thirty-five utility companies currently 
have compressed natural gas-powered vehicle fleets, up from 
only 65 utility companies in 1984. [Ref. 10:p. 49] 

In 1978, the United States Congress passed the 
Natural Gas Policy Act which provided for gradual increases 
in natural gas wellhead price ceilings. The legislation was 
intended to tie the price of natural gas to the projected 
"heat equivalent" price of oil in 1985. By 1985, the 
majority of the natural gas industry was to be decontrolled. 
With the rapid rise of oil prices which occurred in the late 
1970s and early 1980s, the projected prices for natural gas 
in 1985 were quickly exceeded (Ref. ll:p. ix]. In 1986, the 
price of oil dropped and with it the price of natural gas 
also decreased. By early 1987, the price of oil had begun 
to rise drawing the price of natural gas higher also. The 
parallel change in price of both oil and natural gas its 
attributable to the fact that they are substitutes for each 
other. A rise in the price of oil will cause demand for the 
natural gas to increase thereby causing an increase in the 
price of natural gas. 

Since 1978, the percentage increase in the price of 
natural gas has exceeded the percentage increase in the 


price of gasoline. In 1978, the Consumer Price Index for 


a2 


natural gas was 263.1 and the CPI for gasoline was 196.3. 
By 1984, the CPI of natural gas had risen to 584.4, while 
the CPI of gasoline had risen to 370.2. [Ref. 12] 

2. Vehicle Description 

The compressed natural gas vehicle which has proved 
to be the most popular with the general public is actually a 
conversion of a standard gasoline-powered vehicle to a dual 
fuel capable vehicle. Most gasoline-powered vehicles can be 
converted to the compressed natural gas system in one day or 
less. The conversion process does not require any major 
engine modifications. All the conversion parts simply bolt 
on. With the conversion kit installed the vehicle operator 
can drive the vehicle using compressed natural gas fuel or 
gasoline. The switchover procedure from one fuel to the 
other is a simple flip of a switch. [Ref. 13] 

The compressed natural gas conversion kit includes 
the following parts: compressed natural gas cylinders, fuel 
selector switch, regulator, fuel gauge transducer, filling 
connection, gasoline solenoid valve, dual curve ignition 
box, mixer, fuel gauge, master shut off valve, and gas 
Teo nc . The following diagram, Figure 1, shows the major 
parts, their functions, and their installed locations in a 
typical sedan. [Ref. 14:p. 3] 

The natural gas cylinders hold natural gas at a 
pressure of 2400 pounds per square inch. Due to the high 


pressure of the gas, no fuel pump is required to deliver the 


a 


Sriomeamo.) UOTSMOAUO) "| JINDTY 


ms 1 TL Ty 
Sais s Vad 


J rk) 


Vilar 1s 
BAP as. 9 






wee Stee 


Et 


| 


oars 
aANLewissy See a. Ala 


MAINT MY I 
49 4n9 















dan fyi 
44 1.2! 








34 


fuel to the mixer. The regulator controls the flow of 
natural gas from the cylinder(s) to the mixer. The mixer 
bolts onto the carburetor and insures the proper mix of 
natural gas and air is fed into the carburetor and the 
engine. The dual curve ignition box adjusts the ignition 
timing to correspond to the fuel, gasoline or natural gas, 
being fed into the carburetor. The fuel selector switch 
allows the vehicle operator to switch the fuel source of the 
vehicle without stopping the vehicle. The fuel selector 
switch is located on the interior dash of the car as is an 
added natural gas fuel gauge which keeps the driver informed 
as to the amount of natural gas left in the cylinder(s). 
meet. 1l4:p. 3) 
3. Advantages of Compressed Natural Gas Vehicles 

The following are the claimed advantages of a 
compressed natural gas-powered vehicle. 

a. Natural gas iS cheaper per gallon equivalent than 
gasoline. The American Gas Association estimates that 
it is 30 to 60% cheaper to refuel a car with 
compressed natural gas than with gasoline. The 
present cost of a gallon equivalent of natural gas is 
between 45 cents and 85 cents. [Ref. 14:p. 1] 

b. Natural gas burns cleaner than gasoline thus producing 
less pollution. Natural gas burns lead-free and 
produces almost no carbon monoxide. [Ref. 14:p. 1] 

c. Natural gas reduces the maintenance required on 
vehicles. Standard maintenance on vehicles that burn 
natural gas is half that of gasoline-powered vehicles. 
PRof .e44spre 1 | 

dad. Natural gas is plentiful. Consumers don't have to 


worry about any shortage of natural gas in the 
foreseeable future. (Ret i= 14 py .< | 


35 


e. Natural gas is safer than gasoline. Compressed 
natural gas cylinders are built to withstand abuse, 
unlike the conventional vehicle gasoline tank. In the 
event of a gas leak, natural gas, being lighter than 
air, will dissipate rather than pool like gasoline. 
The combustion point of natural gas is 1300 degrees F 
while the combustion point of gasoline is much lower, 
800 degrees F. [Ref. 9:p. 46] 


4. Disadvantages of Compressed Natural Gas Vehicles 
The following are the disadvantages associated with 
converting a vehicle to compressed natural gas. 
a. Few natural gas refueling stations. There are only 
250 private refueling stations and five public 


refueling stations located in the United States. 
(Ref. 9p.) 49) 


b. Limited range with natural gas as fuel. A typical 
compressed natural gas cylinder holds enough fuel to 
allow a range of between 40 to 90 miles. However, 


with the dual fuel capability extended trips can be 
made with a compressed natural gas converted vehicle. 
[Ref. 9:p. 48] 


c. Lower performance. The compressed natural gas-powered 
vehicle loses approximately 10% of its horsepower when 
it operates on natural gas rather than gasoline. 
[Reft. “92p.7-238)] 


ad. High fixed cost to convert vehicle fleet. In order to 
have the ability to refuel a fleet of vehicles, a 
company would have to purchase a cascade compressor 
and its attendent filling station. This capital 
outlay is the most expensive aspect of converting a 
vehicle fleet to compressed natural gas. [Ref. Osioz 
48} 


e. Due to the installation of compressed natural gas 


cylinders in the trunk or storage compartment of the 
vehicle, the cargo capacity of the vehicle is reduced. 


5. Compressed Natural Gas Vehicle Performance Data 
The range of a compressed natural gas-powered 
vehicle while operating on natural gas is a function of the 


number of gas cylinders installed in the vehicle. Each gas 


36 


cylinder allows a range of between 40 and 90 miles, 
depending on the size of the cylinder. However, the dual 
fuel capability of the compressed natural gas-powered 
vehicle allows it to be used for any trip that a 
conventional gasoline-powered vehicle can make. Hoye 1) alsie! 
reason, the compressed natural gas vehicle is considered a 
high performance vehicle in the range performance area. 

The use of compressed natural gas as a fuel results 
in a 10% decrease in the power of the converted internal 
combustion engine vehicle. While this loss of power affects 
acceleration, it can be assumed that all converted vehicles 
are capable of attaining the 55 miles per hour maximum 
cruising speed needed to qualify as a high performance 
vehicle in the cruising speed performance area. 

Based on the range and maximum cruising speed of the 
compressed natural gas-powered vehicle, it is classified as 
a high performance vehicle. 

6. Compressed Natural Gas Vehicle Cost Data 

The initial procurement cost of a compressed natural 
gas-powered vehicle is the sum of the average cost of a 
gasoline-powered vehicle and the average cost of the 
conversion kit. In 1984, the average cost to convert a 
sedan to natural gas for 120 U.S. gas utility company 
vehicle fleets was approximately $1,521, while the average 
cost to convert a van or small truck to natural gas was 


ps9 4 (Ref. 15:p. 22]. The average of these _ two 


37) 


installation costs is $1,555. The 1986 adjusted cost of 
installation, using the adjustment factors in Table 1, is 
$1,628 ((1555/3012 2) eee ore Therefore, the initial 


procurement cost of the vehicle used in this thesis is: 


Average cost of gasoline vehicle + $1,628 


While the installation of the conversion kit adds some value 
to the vehicle, the salvage value will be estimated at 10% 
of the initial procurement cost of the gasoline-powered 
vehicle before conversion took place. 

Since this thesis 1S concerned with fleet vehicles, 
a decision to convert to compressed natural gas-vehicles 
would require the purchase of a cascade compressor and 
filling “station. A 30 cubic foot per minute (CFM) cascade 
compressor refueling system, capable of refueling 30 
vehicles at a time, would cost $75,000 [Ref. 16:p. 8]. In 
1982, a cascade compressor and filling station capable of 
refueling nine vehicles per hour would cost approximately 
$44,000 installed [ReEf. 6 :ppreysé Saiz A small compressor 
capable of handling one or two vehicles per hour would cost 
around $7,000 installed {Ref. 1423p 2978 The small 
compressor would take too long to refuel vehicles while the 
30 CFM compressor would probably exceed the refueling 
requirements of most Navy commands. Therefore, the 


investment cost for the compressor and filling station used 


38 


in this thesis will be the $44,000 option adjusted to 1986 
gdomlars (1.e., $49,570). 

As of 28 February 1986, the national average price 
for a gallon equivalent of natural gas was 93 cents. The 
cost of natural gas to vehicle fleet users was $0.72 ona 
national average basis. The average small truck or van will 
get around 15 miles per gallon. Therefore, the average cost 
of fuel per mile of operation for a compressed natural gas- 
powered vehicle is approximately five cents for fleet users. 
[Ref. 16:p. 2] 

The American Gas Association claims that the 
maintenance costs of compressed natural gas-powered vehicles 
is half that of gasoline-powered vehicles [Ref. 14:p. 1]. 
This claim is based on the fact that natural gas is a clean 
buemning fuel so oil, spark plugs, and points will not 
require changing as often as in a gasoline-powered vehicle. 
In Mr. Hamilton's review of internal combustion engine 
maintenance costs, he found that the ignition system 
maintenance costs and the lubrication costs amounted to 
roughly 14% of the total maintenance cost of an internal 
combustion engine vehicle [Ref. 7:p. 740]. Therefore, an 
extension of the life of the oil, spark plugs, and points to 
double their normal life would only result in a savings of 
7% of the maintenance cost. For the purposes of this 


thesis, the maintenance cost of natural gas vehicles will be 


39 


estimated at 75 percent of the maintenance cost of gasoline- 
powered vehicles. 

The conversion kit's useful life is at least equal 
to the life of the vehicle in which it is installed [Ref. 
6:p. 57]. The American Gas Association estimates the useful 
life of the compressor to be 10 years with annual operations 
and maintenance expenses for the compressor being equal to 
12 cents per gallon equivalent of natural gas pumped [Ref. 


ey a 


40 


(Meee tobe  CrCbE COS) MODEL 


Department of Defense Instruction 7041.3, dated 18 

October 1972, defines economic analysis as: 
A systematic approach to the problem of choosing how to 
employ scarce resources and an investigation of the full 
implications of achieving a given objective in the most 
efficient and effective manner. 
The instruction goes on to require an economic analysis be 
performed for proposals whenever there is a "choice or 
trade-off between two or more options even when one of the 
options is to maintain the status quo or to do nothing." 
Beets 128: pp. 2-3] 

A major portion of the economic analysis is the cost 
analysis. DOD Instruction 7041.3 requires that life cycle 
cost estimates be prepared for all program alternatives when 
feasible. The instruction defines life cycle costs to 
include "all anticipated expenditures directly or indirectly 
associated with an alternative." The InSserUuection 
specifically states that "sunk costs," costs which have 
already been incurred prior to conducting the analysis, are 
excluded from the cost analysis. [Ref. 18:p. 2] 

The life cycle cost estimate begins with an estimate of 
outlays for each year of the "economic life" of the 
alternative. The economic life of an alternative is the 
period of time that an alternative is capable of providing 


the service it was designed for. [Ref. 18:p. 7] 


4Al 


Once the yearly outlay estimates have been made, a 
discount factor is applied to each year's outlays to 
determine the net present value of the alternative. The 
discount factor is used to recognize that there are 
differences in the timing of expenditures. A dollar spent 
today 1S more valuable than a dollar that will be spent two 
years from today. {Refs 18: ppe, S67] 

In the civilian business environment, the discount 
factor is based on the cost of acquiring additional capital. 
In the Department of Defense, the discount factor is based 
on a 10% interest rate. The discount factors for the 


Department of Defense are listed in Table 2. [Ref. 18:p. 6] 


TABLE 2 


DEPARTMENT OF DEFENSE DISCOUNT FACTORS 


Present Value of $l 


Project Year 10% Discount Factor 

ili 0.954 

Z O=2S67, 

3 0.788 

4 Sls Wik y 

5 0.652 

6 02592 

7 O53 36 

8 0.489 

9 0.445 

10 0.405 
Source: Department of Defense Instruction 7041.3, 


dated 18 October 1972. 


42 


The alternative which is found to have the lowest 
average cost per year is considered to be the most 


SEelewent. [|Ref. @e2p2e7) 


Pee GLFE CYCLE COST COMPONENTS 
The major groups of costs which can be included in a 
life cycle cost estimate are: 
1. Research and development costs 
2. Investment costs 
3. Operations costs. [Ref. 18:pp. 2-5] 

The Department of Defense has not invested funds in the 
research and development of either electric-powered vehicles 
Or compressed natural gas-powered vehicles, so research and 
development funds will not be entered into the life cycle 
eest Lormula. 

Investment costs are costs associated with the purchase 
of real property, equipment, non-recurring services or 
operations, and maintenance start-up costs. Investment 
costs do not necessarily occur in only Year 1 of a 
procurement. 

Investment costs can be either fixed or variable. Fixed 
investment costs equate to fixed costs in the civilian 
business environment as they are the fixed cost of choosing 
a particular alternative. Being a fixed cost, the amount 
does not vary with units of production, or in the case of 


this thesis, vehicles in a particular fuel category. An 


43 


example of a fixed investment cost would be a refueling 
station. {Refs “19% pnw] 


Variable investment costs are tied to the volume GLE 


option. An example of a variable investment cost is the 
initial procurement cost of a vehicle. The variable 
investment cost rises with each vehicle procured. (Ref. 
LJs Dp.) /4 | 


Operations costs, or recurring costs, are costs such as 
personnel, material consumed during operations, overhead, 
operating expenses and other annual expenses. The choice of 
either of the alternative vehicles for use in the fleet 
would not necessitate any additional personnel or overhead. 
The recurring cost affected would be material consumed, 
mainly fuel and maintenance costs. [Ref. 18:pp. 4-5] 

Recurring costs such as fuel and maintenance costs are 
classified as variable costs by civilian businesses in that 
they vary directly with the units of output or, in the case 
of this thesis, the number of vehicles in a particular fuel 
category. Another common business term for variable costs 


1s direct costs. ‘“[Ref. 192p. (7a 


Be LIFE CYCLE COST FORMULA 

The following life cycle cost formula was presented by 
Dr. Dan Boger of the Naval Postgraduate School at the 
Defense Logistics Agency Operations Research and Economic 
Analysis Workshop in Virginia Beach, Virginia, on 6 December 


Toe5. The ~title— “of pr. Boger's presentation was 


44 


"Alternative Vehicle Propulsion and the Optimal Industrial 


Fleet." [Ref. 20] 
Lecis = fiz + CijXij 
where: 


1 = vehicle type 


J = propulsion type 


LCCi4 = life cycle cost for alternative i,j 
fj = fixed investment for alternative i,j 
Cij = unit variable LCC for alternative i,j 
Xj4j = number of units of alternative i,j. 


The formula gives the user the option to deal with 
various types of vehicles. Due to data limitations at the 
Naval Postgraduate School Transportation Office, this thesis 
will deal only with different types of propulsion, therefore 
the i variable will not change. 

The total life cycle cost formula is broken down into 
two sub-formulas. The first sub-formula is used to compute 
the unit variable life cycle cost for the alternative i,j. 
st 


Jk 
Cij = Pijo + eerie * ey 


where: 


Pijo = unit procurement cost of alternative i,j 


OCijt = unit operating cost of alternative i,j in year t 


45 


st = discount factor in year t 


Sjj = unit salvage value for alternative i,j 


KF 
ll 


the number of years in the economic life of the 
vehicle. 


The second sub-formula is used to calculate the unit 


operating cost of alternative i,j in year t. 


where: 


Cit = ™itleje eee eee 


Mj;+ = annual miles for vehicle type i in year t 


est = cost/mile for fuel of type j in year t 
Nijt = maintenance cost/mile for alternative i,j in 
year t 


Pijt = unit procurement costs for alternative i,j 


in year t. 


C. GASOLINE-POWERED VEHICLE LIFE CYCLE COST 


The best way to explain the use of the life cycle cost 


formula and its sub-formula is through an example. The 


gasoline-powered vehicle will be classified as propulsion 


type 1. The following data were gained through a review of 


the 1986 records of the transportation office of the Naval 


Postgraduate School [Rets. 21,22]. 


1 


Zi 


Number of vehicles subject to study: 62 


Total initial procurement (investment) cost of subject 
vehicles in 1986 dollars: $506,274 


Total miles driven by subject vehicles in 1986: 
313,000 


Total fuel cost for subject vehicles in 1986:) 5177557 


46 


Total maintenance cost for subject vehicles in 1986: 
2736s 


Estimated average economical life fone subject 
vehicles: 8 years 


Estimated average salvage value for subject vehicles: 
10% of initial procurement cost. 


Using the above data, the life cycle cost for gasoline 


vehicles at the Naval Postgraduate School is computed as 


follows: 


ie 


Beginning with the sub-formula for unit operating cost 
of alternative i,1 in year t, computations are as 
follows: 


as snnucshemmhes for vehicle type + in year t (m;+) 


Benoa | 
—75-— = 5048 miles 


Pe occ iiehe FOtmerlclor type 1 am year — (e+) 


do 


c. Maintenance cost/mile for alternative i,1 in year 
e (jit) 


Za Oe 


dad. There are no unit procurement costs in any year 
other than year 0 so pjj+ = O. 
Using the figures computed above the unit 
operating cost of gasoline vehicles in year t is: 


Oj1t = 5048(.0561 + .0874) + 0 = $724 


The next step is to compute the unit variable life 
cycle cost for the gasoline alternative (cj). 


47 


a. The initial unit procurement cost of gasoline 
vehicles in years OM nig) aeeoe 


506,274 
=~5 ae = $87 oe 


b. Next, the unit operating cost computed previously 
is multiplied by the discount factors for years 
one through eight, its economic life. The 
products are then added together to get the total 
discounted operating cost for the economic life of 
the vehicle. 


al 


Y o4,tst = ((724 x .954) + (724 x .867) + (724 x .788) 
t=1 ss. t(724 com 
= $4,053 

The total discounted fuel cost was $1,584, while 
the discounted maintenance cost was $2,469. 

c. The unit salvage value is the estimated salvage 
value of the vehicle times the discount factor in 
the year it is salvaged. The gasoline-powered 


vehicle has an eight year economic life with a 
Salvage value of 10% of its initial procurement 
cost. The initial procurement cost was $8,166, so 
its salvage value is $817 x .489, the discount 
factor in year eight. Therefore, 


§ls;, = $400 


Putting the above computations into the formula, the 
unit variable life cycle cost for the gasoline-powered 


vehicle equals: 
8,166 + 4,053 - 400 = $11,819 


3. The final step in computing the life cycle cost for 
the gasoline vehicle alternative is to figure out the 
fixed investment costs for the alternative and the 
number of vehicles using gasoline. The fixed 
investment cost of choosing gasoline equals zero. 


48 


This is due to the prior purchase of all the equipment 
and facilities required to maintain and operate the 
gasoline vehicles. These prior expenditures are now 
considered "sunk costs" and are excluded from the cost 
analysis. The number of vehicles using gasoline in 
the optimal solution is unknown. Thus the final life 
cycle cost formula for the gasoline-powered vehicle 
Option 1s: 


O° + 11,819xj4 


Bo BLECTRIC—-POWERED VEHICLE LIFE CYCLE COST 

The life cycle cost for the electric-powered vehicle 
will be derived by using the cost data that were determined 
in Chapter II. The electric-powered vehicle will be 
classified as propulsion type 2. 

The computations for the unit operating cost of the 
electric-powered vehicle in year t are as follows: 


1. Annual miles for vehicle type 2 are the same as the 
gasoline-powered vehicle, 5048 miles. 


2. The fuel efficiency rating of the electric vehicle is 
1.11 kilowatt hours per mile of operation. The cost 
to the Naval Postgraduate School for a kilowatt hour 
Siwclectrewerty se rougniy SO0708, according to the 
Public Works Office. Therefore, the cost/mile for 
fuel is: 


1.11 x .08 = $0.0888 


3. It was decided in Chapter II that the maintenance cost 
of the electric vehicle would be estimated at 65% of 
the maintenance cost of the gasoline-powered vehicle. 
The gasoline-powered vehicle maintenance cost per mile 
was determined to be  $0.0874. Therefore, the 
maintenance cost per mile of operation for the 
electric-powered vehicle is: 


sOomeeOG74 = 50.0568 


49 


4. Due to the 10 year economic life of the battery 
charger it will not have to be replaced during the 
life of the vehicle. The batteries have an estimated 
life of 10,800 miles. Based on the average annual 
miles of 5048, the batteries would require replacement 
every 2.14 years or roughly every two years. The 
replacement cost was estimated to be $2,000 in 1979, 
this equates to $2996 in 1986, based on the "All 


Items" consumer price index in Table 1. Battery 
replacement expense of $2,996 should be expected in 
years 3, 5, 7, and 9 of the analysis. If the 


experimental nickel-zinc batteries are perfected, the 
batteries would have to be replaced every seven years 
at a replacement cost of $2,980. 

Putting the above data into the unit operating cost formula, 


the unit operating cost for an electric-powered vehicle in 


years 1, 2, 4, 6, 8, and 10, is determined to be: 


5048(.0888 + 20568) + )05— S7ea 


In years 3, 5, 7, and 9, the unit operating cost for an 


electric-powered vehicle is found to be: 


5048(.0888 + .0568) + 2,996 = $3,731 


The unit variable life cycle cost for the electric 
vehicle is computed as follows: 


1. The initial procurement cost of the electric vehicle 
was estimated to be 1.5 times the initial procurement 
cost of the gasoline-powered vehicle. The initial 
procurement cost of the gasoline-powered vehicle was 
determine to be $8,166. Therefore, the initial 
procurement cost of the electric-powered vehicle is: 


1.5 x 8,166 = $12,249 
This initial procurement cost includes a battery 


charger. 


50 


The wnt emm@peratingescost™ for the electric vehicle 
($735) is multiplied by the discount factors for each 
appltedable== year), 2, 4,6, 8, 10) and the unit 
operating cost including battery replacement ($3731) 
for years 3, 5, 7, and 9, is multiplied by the 
appropriate discount factors. For years 1, 2, 4, 6, 
8, and 10, the computations would be: 


((735 x .954) + (735 x .867) + (735 x .717) + 
(735 x .592) + (735 xX .489) + (735 x .405)) 


The sum of these products is $2,956. For years 3, 5, 
7, and 9, the computations are: 


(esl sore 7SS yee (s7emes 1.652) + (3731 x .538) 
+ (3731 x .445)) 


The sum of these products is $9,039. The sum total 
for all the years of the electric vehicle's economic 
life is $11,995. Of this total, fuel cost amounts to 
$2,886, and maintenance, which includes replacing the 
batteries, amounts to $9,109. 


The salvage value of the electric-powered vehicle was 
estimated to be six percent of the initial procurement 
cost of the vehicle. Therefore, the unit salvage 
value equals ((12,249 x .06) x .405) = $298. 


inserting the above computations into the unit 


variable life cycle cost formula, the ten year unit life 


cycle cost for the electric vehicle is determined to be: 


12,249 + 11,995 - 298 = $23,946 


To find the eight year life cycle cost, the ten year unit 
life cycle cost is divided by 10, then the quotient is 
multiplied by eight. The resulting eight year unit life 
cycle cost is $19,157. The eight year unit life cycle cost 
for fuel would be $2,309, with the eight year unit life 


cycle cost for maintenance totalling $7,287. 


Sl 


The next step is to compute the life cycle cost for the 
electric-powered vehicle alternative. Here the cost of 
making the decision to use electric-powered vehicles is 
recognized. The cost of making the decision is equal to the 
cost of procuring the vehicles plus the cost of procuring 
Support equipment or facilities. 

The cost to procure a battery charger is included in the 
vehicle procurement ' cost. No special facilities are 
required as the battery charger can run off standard 
electric current of 110 volts. Therefore, the life cycle 
cost formula for the electric-powered vehicle alternative 


ne. 


O + 19,157x45 


E. COMPRESSED NATURAL GAS-POWERED VEHICLE LIFE CYCLE COST 
The compressed natural gas-powered vehicle will be 
classified as propulsion type 3. Its life cycle costs will 
computed using the cost figure derived in Chapter II. 
The unit operating cost of alternative i,3 in year t is 
computed as follows: 
1. Annual miles for the vehicle type is 5048 miles. 


2. The fuel cost per mile is $0.05. 


3. The maintenance cost per mile was estimated to be 75% 
of the gasoline vehicle, .0874 x .75 = .066. 
4. The only unit procurement costs occur in year 0. 


Therefore, the unit operating cost of a compressed 
natural gas-powered vehicle in year t = 


5048 (.05 + .066) + 0 = $586. 


D2 


The unit variable life cycle cost for the compressed 
natural gas-powered vehicle is computed below: 


1. The initial procurement cost of the compressed natural 
gas vehicle was estimated to be the initial 
procurement price of a gasoline-powered vehicle plus 
$1,628. Therefore, the initial procurement cost of a 
compressed natural gas vehicle is: 


8,166 + 1,628 = $9,794. 


2. The sum total of the compressed natural gas vehicle's 
unit operating cost of $586 times the discount factors 
in its eight year economic life is $3,280. The fuel 
cost portion of this total is $1,410, while 
maintenance costs amount to $1,870 during the eight 
year economic life. 


3. The salvage value of $817 times the discount factor in 
year eight of .489 yields a unit salvage value of 
$400, the same as that of the gasoline-powered 
vehicle. 


Putting the above computations into the life cycle 
cost formula, the life cycle cost for the compressed natural 


gas-powered vehicle is determined to be: 


9,794 + 3,280 - 400 = $12,674 


The life cycle cost for adopting the compressed natural 
gas vehicle into the Naval Postgraduate School vehicle fleet 
would be the fixed investment cost of building and equipping 
a compressed natural gas refueling station plus the variable 
life cycle cost of a compressed natural gas vehicle times 
the number of compressed natural gas vehicles in the fleet. 
The compressed natural gas refueling station was determined 


bemeecOst $44,000 in 1982 or $49,570 in 1986 dollars. 


3 


Therefore, the life cycle cost of the compressed natural gas 


vehicle alternative ws: 


49,570 + 12,674xj43- 


Life cycle cost computation worksheets are included as 


the Appendix of the thesis. 


54 


IV. THE LINEAR PROGRAMMING MODEL 


Linear programming is an advanced mathematical 


programming technique which has found wide use in the 


business environment. It deals only with problems where the 
relationships between the variables are linear. For 
example, when a vehicle is purchased a price is paid. cles 


two of the vehicles are purchased, the purchaser would have 


to pay twice as much. The relationship between price and 
quantity in this example is a linear relationship. (Ref. 
ep. 2) 


Linear programming was developed in the late 1940s by 
Professor G. Dantzig. It was widely used in the late 1950s 
by petroleum companies to determine the best mix of gasoline 
and heating oil the companies should produce in order to 
maximize their profits. Various linear programming models 
were developed to help the petroleum companies deal with 
pipeline and tanker problems. [Ref. 23:p. 2] 

Linear programming provides business managers a 
mathematical tool to help them allocate scarce resources to 
achieve an objective. Some examples of objectives would be 
to maximize profit or minimize costs. Linear programming 
will find the very best solution to a given problem and it 
will indicate when there are equally good alternative 


semtr1ons. (Ref. 23:p. 2] 


22 


The business manager uses linear programming by looking 
at a real world problem and describing it in a mathematical 
model which consists of a linear objective function and 
linear resource constraints. [Ref. 24:p. 25} 

The three principal steps in developing a linear 
programming model are: 

(1) the identification of solution variables (the 
quantity of the activity in question), 

(2) the development of an objective function that is a 
linear relationship of the solution variables, and 

(3) the determination of system constraints, which are 
also linear relationships of the decision variables, 
that reflect the limited resources of the problem. 
(Ref. 24:p. 26] 

Due to the fixed investment that would ensue if 
compressed natural gas-powered vehicles were used in the 
fleet, the fixed charge integer linear programming model 
will be used in this thesis. In an integer linear program, 
some or all of the solution variables are required to be 
integers. [Refs 25:p. vi) 

Integer programming was pioneered in the late 1950s by 
Ralph Gomory. The advantage of an integer program is that 
the solution will be in integer form. With a non-integer 
linear program, non-integer solutions are often computed. 
In this thesis, a non-integer solution would not be helpful 
as one cannot use half a vehicle. [Ref. 25:p. vii] 

In fixed charge problems, if the decision made is to go 
with an alternative, there is a fixed charge inherent in 


making that decision [Ref. 25:p. 18]. In this thesis, the 


fixed charge would be the cost of building and equipping the 


56 


compressed natural gas refueling station. Even before one 
vehicle has joined the vehicle fleet, there would be an 
expenditure of funds which is not a linear cost of operating 
the compressed natural gas vehicle. 

In setting up a fixed charge model, a decision variable 
is put in the objective function. The decision variable has 
two values, 1 or O. If the value of the decision variable 
is 1, the alternative is adopted and the fixed charge will 
be expended. If the value of the decision variable is 0, 
then the alternative is rejected and the fixed charge is 


bypassed. 


A. FIXED CHARGE INTEGER LINEAR PROGRAM MODEL 

In his presentation at the Defense Logistics Agency 
Workshop, Dr. Dan Boger explained the following integer 
programming model which can be used for deriving the optimal 
vehicle fleet. [Ref. 26] 


The integer programming model is: 
minimize ) ee fa Ve 
Ls Mia 2 J ab yy 

subject to the following constraints: 


(1) 2 2 Pijoxij + fij¥ij < Po 
1 oJ 


t=8 


(| c~7 II 


(2) i) eijtxij < E 


ic aa 


ao) 


t=8 
ee) ete) Ss 
C= 
(4) ie er 
(5) oi eee cia 
(6) Peay =F 
i oJ 
where: 
Ci; = unit variable life cycle cost for alternative i,j 
xij = integer number of units of alternative i,j 
fi4 = fixed investment costs for alternative i,j 
Vij = decision variable for alternative i,j 
Pijo = unit procurement costs in year O for alternative 
1,) 
Cijt = fuel costs in year t for alternative i,) 


E = total fuel costs for eight year life cycle for 
all fleet vehicles 


mMijt = maintenance costs in year t for alternative i,j 


M = total maintenance costs for eight year life cycle 
for all fleet vehicles 


Po = total investment costs in year 0 
ujj = upper limit on number of units of alternative i,j 
1ij = lower limit on number of units of alternative i1,j 


F = number of vehicles in vehicle fleet 


The fixed charge objective function for the above 
integer programming model is: 


Mamaml Ze a) Cy sc neeer nye 
al 


58 


where: 


ee Oman 1S saneinteger 
Vem =O. Or 1 


ele VY 3 uaa 0 


The following budget and performance constraints were 
placed on the optimal vehicle mix for the Naval Postgraduate 
School vehicle fleet [Ref. 27]: 


1. At least 30 of the 62 vehicles must be gasoline- 
powered in order to meet current vehicle taskings. 


2. Fleet life cycle fuel expenditures must not exceed 
$189,000. 
3. Fleet life cycle maintenance expenditures must not 


exceed $183,000. 
Inserting the values for the variables which were 
computed in Chapter III and the budget and performance 
constraints delineated above, the vehicle mix formulation 


problem becomes: 
Meemimize 11819x, + 19157x5 + 12674x3 + Oy, + Oyo + 49570y, 
subject to 


(1) 8166x, + 9799x5 + 9794x3 + Oy, + Oy + 49570y3 < 540,000 


(2) 1584x, + 2309x> + 1410x; < 189,000 
(3) 2469x, + 7287x5 + 1870x3 129, C00 
(4) x7 = Olay <0 


a9 


(5) X95 -32y> <0 
(6) X3 ="O2ZY3 < 0 
Cy) aed) oe +30yYj < O 


The first constraint is a budget constraint on the total 
investment cost in year 0. The constraint covers both fixed 
investment and variable investment costs. The right hand 
Side value of the constraint is derived by computing a 95% 
confidence interval for vehicle procurement costs for the 
Naval Postgraduate School fleet of 62 vehicles. 

The second constraint is a budget constraint on the 
amount of funds that can be spent on fuel during the eight 
year life of the fleet vehicles. The right hand side of the 
constraint is computed using a 95% confidence interval based 
on 1986 Naval Postgraduate School fuel expenditures. 

The third constraint is also a budget constraint but it 
limits the amount of funds which can be spent to maintain 
the 62 vehicle fleet during its eight year life cycle. The 
right hand side is computed using a 95% confidence interval 
based on the 1986 maintenance costs for the Naval 
Postgraduate School fleet of 62 vehicles. 

The fourth through seventh constraints are on the number 
of vehicles of each fuel type that may be included in the 
optimal fleet mix. The fourth constraint limits the number 
of gasoline-powered vehicles that may be included in the 


optimal max to 62. The fifth constraint limits the number 


60 


of electric-powered vehicles that may be in the optimal mix 
to 32. This coincides with the operational requirement that 
at least 30 of the 62 vehicles be gasoline-powered. The 
sixth constraint limits the number of compressed natural 
gas-powered vehicles to 62. All vehicles in the optimal mix 
may be compressed natural gas vehicles due to their dual 
fuel capability. The seventh constraint insures that at 
least 30 of the vehicles in the optimal mix are capable of 
using gasoline as a fuel source. 

When the above problem was run through the integer 
program, the optimal mix of vehicles was computed to be 62 
gasoline-powered vehicles. The net present cost of 
purchasing, operating and maintaining these vehicles for an 
eight year life was computed to be $732,778. 

The above integer program would be useful to the Navy 
Transportation Officer if he were to have control of the 
funds required to procure the vehicles for his command. 
However, the Naval Facilities Engineering Command, 
Chesapeake Division (ChesDiv), located in Washington, D.C., 
is the central procurement activity for vehicles for the 
Navy. Vehicles purchased by cChesDiv are sent to Navy 
commands, who then make decisions as to what vehicles will 
be retired from service. The individual command 
transportation officers do not have an input into the 
procurement process unless they require a vehicle in 


addition to their present allowance. 


61 


The funds required to build a compressed natural gas 
refueling station would be justified through a one time 
budget augment request consisting of a request for Other 
Procurement, Navy (OPN) funds and minor construction funds. 
The budget augment request would be filed through the 
command's chain of command during the annual budget cycle. 
The justification for these funds would be a projected 
Savings due to the use of alternative fuels rather than 
gasoline in fleet vehicles. 

In order to approach the optimal mix problem from the 
viewpoint of the individual command transportation officer, 


the following integer program is proposed: 


Minimize 4053X, + 9596X5> + 3280x5 + Oy) + Oyen 
Subject to 

(1) 1584x, + 2309x5 + 1410x3 < 189,000 
(2) 2469x, + 7287x5 + 1870x3 < 183,000 
(3) X71 - 62y) < 0 

(4) X95 ae yO <a 

C5) X3 - 6230 

(6) =a) — Xa 43 0v < 0 


This integer program recognizes only the funds that the 


individual command has control over. The objective function 


62 


consists of the life cycle fuel and maintenance costs 
attributable to each of the vehicle propulsion types and 
ignores salvage values because these funds are not returned 
to the command disposing of the vehicle. 

The constraints are the same as the first integer 
program with the exception that the constraint dealing with 
initial investment costs is deleted since the command has no 
control over these funds. 

The optimal mix derived from this integer program would 
provide the lowest cost vehicle fleet in terms of annual 
Operations and Maintenance, Navy funds. 

When the above formulated problem is run through the 
integer program, the optimal solution is found to be 62 
compressed natural gas-powered vehicles. The O&M,N cost of 
operating the 62 vehicle fleet of compressed natural gas 
vehicles for the eight year life of the vehicles would be 
£203,360. 

A third situation to consider is the establishment of a 
new transportation fleet at a base where no refueling 
Capabilities presently exist. The cost of building a two- 
pump gasoline refueling station is estimated to be $150,000 
(Ref. 28]. Assuming that the experimental nickel-zZinc 
batteries were installed in the electric vehicle, the 


problem would be formulated as follows: 


63 


LiSdox a 4655 x50 1267 4x33 150000y 4 + OY5 + 49570Y3 


subject to 

8166x, + 9799x> + 9794x3 + 150000y, + Oyy + 49570y3 < 660000 
1584x, + 2309x> + 1410x3 < 189000 
2469X%4 °F 9 2763x%5 54 oo Ox, < 183000 

“7 = OZ yaa < 0 

X5 - 32y5 <0 

x3 - 62y3 <0 

~x4 - Xz + 30y) ne 


When the above problem was run through the integer 
program, the optimal vehicle mix was found to be 62 
compressed natural gas vehicles. The net present cost of 
procuring, operating and maintaining the fleet was computed 


to be $835,358. 


Bs SUMMARY AND CONCLUSIONS 

This thesis has developed and explained a model for 
determining the life cycle cost of alternative fuel 
vehicles. Using the life cycle cost and requirement data 
particular to a command, the integer linear program model 
can be used to determine the optimal mix of vehicles for the 


command's transportation fleet. 


64 


The thesis has looked at three ways the models can be 
used. The first case was that of an established base with a 
gasoline refueling station in operation. Due to the high 
cost of procuring the compressed natural gas refueling 
station and the high life cycle cost of the electric 
vehicle, the optimal solution was found to be an entire 
fleet of gasoline vehicles. 

The second case looked at minimizing the = annual 
operations and maintenance expenditures on the 
transportation fleet while ignoring the initial investment 
costs. The integer program found a fleet of compressed 
natural gas vehicles would require the least expenditure of 
operations and maintenance funds. 

The third case looked at the problem of establishing a 
new transportation fleet at a base which does not have any 
refueling capabilities at the present time. The high cost 
of the gasoline refueling station more than offsets the cost 
of the compressor and conversion kits for the compressed 
natural gas vehicles. Again, the optimal solution was found 
to be an entire fleet of compressed natural gas vehicles. 

The electric vehicle was found to have much too high a 
life cycle cost to enter into the optimal mix, even though 
it had no fixed investment cost. In the third case, the 
experimental batteries were factored into the life cycle 
cost but the reduction in life cycle cost was still too 


small to make the electric vehicle an economic solution. 


63 


The compressed natural gas vehicle appears to be a 
feasible alternative to the gasoline vehicle. The factors 
which seem to impair its competition with the gasoline 
vehicle are: 

1. The scarcity of compressed natural gas refueling 
stations. The number of refueling stations would not 


be expected to increase until the number of vehicles 
using compressed natural gas increases. 


2. The price of natural gas, a relatively abundant 
natural resource, is tied to the price of petroleun, 
an increasingly scarce natural resource, by the 


Natural Gas Policy Act of 1978. With this dependency 
on the price of oil, the price of natural gas is 
inflated to a level which does not justify the 
additional investment in conversion kite and 
compressed natural gas refueling stations for little 
or no savings will accrue. 

3. The high cost of the conversion kits. The conversion 
kits are specialty items not offered by automobile 
manufacturers, thus the cost is high and the 
maintenance or conversion kit parts is very 
specialized. 

The above factors are interrelated with the price of 
natural gas being the major obstacle in the compressed 
natural gas vehicle's future. If the price of natural gas 
can drop to a level significantly below that of gasoline, 
its attractiveness as a vehicle fuel will increase. Savings 
from lower fuel costs would justify investment expenditures 
by large businesses, state and local governments. This 
would increase the number of CNG-vehicles on the road, 
leading to an increase in compressed natural gas refueling 
stations. Increased popularity of compressed natural gas 


would lead automobile manufacturers to offer factory 


equipped CNG-vehicles. The mass production of the CNG- 


66 


vehicle would lower the additional cost for the CNG- 
conversion kit as well as increase the number of maintenance 


facilities capable of repairing CNG conversion systems. 


67 


APPENDIX 


VEHICLE LIFE CYCLE COST COMEUTZA LIONS 


Item 0 


Fixed 
Invest. 0 


Vehicle 
Invest. 8166 


Fuel 
Cost 


Daseounte 
Factor 


Dirse- 
Fuel 
Cost 


Maint. 
Cost 


Pase. 


Maint. 
Cost 


Salvage Cost 


GASOLINE-POWERED VEHICLE 


LIFE CYCLE COST COMPUTA Peis 


283 


~954 


276 


Total 


441 


421 


Year 


2 3 + 


235 Zoo Zio 


so O/. se 2 OS .  agely 


245 225 203 
Discounted Fuel 


441 441 441 


382 348 316 


Zo5 283 283 “Zee 


-652 .592 .538 3eiae 


185 168 152 _ 


Cost = $1,584 


441 441 441 441 


288 261 23/ 2ake 


Total Discounted Maintenance Cost = $2,469 


Discounted Salvage Cost 


Disc. 
Yearly 
Cashflows 


Discounted Unit Life Cycle Cost = $11, 


Discounted Alternative Life Cycle Cost 


8166 


690) 627 al 


67 


(817) 


(400) 


473 429 389 (46) 
819 


= 0 ye ldeae sr 


Pit Ge lRane— POWERED VEHICLE 


Mp eeerels COST COMPUTATIONS 


Year 
Item 0 alt 2 3 4 5 6 7 8 9 LO 
Fixed 
Invest. 0 
Vehicle 
Invest. 12249 
Fuel Cost 448 448 448 448 448 448 448 448 448 448 
Discount 
Baccor Dopo G ee 7 Gomme To oOo e. 2.592 .538 .489 .445 .405 
Discounted 
Fuel Cost ADY 388 BS Be 292 265 241 219 199 181 


Total Discounted Fuel Cost = $2,886 
Maint. Cost 287 287 287 287 287 287 287 287 287 287 
Discounted 


Maint. Cost 274 249 226 ZUG 187 ile 154 140 Zs 116 
Total Discounted Maintenance Cost = $1,850 


Battery 

Repl. Cost 2996 2996 2996 2996 

Discounted 

Battery Cost eco wo Ss EG Ae2 i323 
Total Discounted Battery Cost = $7,259 

Salvage Cost (735) 

Discounted Salvage Cost (298) 

Disc. 

Yearly 


mesmei. 12249 701 637 2940 527 2432 435 2007 359 1660 (1) 
Discounted 10 Year Life Cycle Cost = $23,946 

Discounted 8 Year Life Cycle Cost = (23,946/10) x 8 = $19,157 
8 Year Life Cycle Vehicle Cost = (12249/10) x 8 = $9,799 


8 Year Life cycle Fuel Cost = (2886/10) x 8 = $2,309 


68 


ELECTRICG=POWERED a ede ane: 
LIFE CYCLE COST COMPUTATIONS S(eelianvEr, 


8 Year Life Cycle Maint. Cost (incl. Batteries) 
= ((1850 + 7259/10) 8 = Size 


Discounted Alternative Life Cycle Cost —- Gai ie. 


69 


COMPRESSED NATURAL GAS-POWERED VEHICLE 


PUR Ewe ce LESeOST <COMPUTATIONS 


Year 
Item 0 1 Z 3 4 5 6 7 8 
Fixed 
Invest. 49570 
Vehicle 
Invest. 9794 
Fuel Cost 252 2 Ore AS 2 252 2512 ZO Zo 252 
Discount 
Factor ~954 -867 -788 ary mG 5 2 O92 S56 ~-489 
biscounted 
Fuel Cost 240 eS 199 181 164 149 136 ie 
Total Discounted Fuel Cost = $1,410 
Maintenance 
Cost Ses S135 333 SoS 383 535 353 333 
Discounted 
Maint. Cost 318 289 262 239 247 197 179 163 
Total Discounted Maintenance Cost = $1,864 
Salvage Cost (317 ) 
Discounted Salvage Cost (400) 


Discounted Unit 

Yearly 

Cashflows 9794 558 5107 461 420 381 346 Ba. C4) 
Discounted Unit Life Cycle Cost = $12,668 

Discounted Alternative Life Cycle Cost = 49,570 + 12,668x3 


Note: Difference in unit life cycle cost from text is due to 
rounding of numbers. 


70 


LO; 


de 


2 


LS 


14. 


LIST OF -REEERENCES 


"The Road Vehicle: Today and Tomorrow," Electric 
Vehicles, V. 64, N- 27 -0une. 1972 


Stuhlinger, Ernst, "Electric Automobiles--Ready for the 


Market?" 18th Intersociety Energy Conversion 
Engineering Conference, V. 3, 1983. 


Noyes Data Corporation, Electric and Hybrid Vehicles, 
lo 9. 


Hamilton, William, Electric Automobiles, McGraw-Hill 
BOOK “Company ,1960: 


Unnewehr, eB. and Nasar, S cao Electric Vehicle 
Technology, John Wiley & Sons, Inc., 1982. 


Garrison, Clifton F. Jr., Decision Models for Conducting 
an Economic Analysis of Alternative Fuels for the ICE 
Engine, Ma S.M. Thesis, Naval Postgraduate School, 
Monterey, California, March 1983. 


Hamilton, William, "Costs of Electric Vehicles in Local 


Fleet Service," 19th Intersociety of Energy Conversion 
Engineering Conference, V. 2, 1984. 


Telephone interview with Dr. Patil, U.S. Department of 
Energy, Washington, D.C., 23 March 1987. 


Watls, dic; "Compressed Natural Gas Could Replace 
Gasoline as Vehicle Fuel of the Future," Pipeline & Gas 
Journal, January 1986. 


American Gas Association, Natural Gas Vehicles Market, 
1936. 


iS. Congress, Congressional Budget Office, 
Understanding Natural Gas Price Decontrol, March 1983. 


U.S. Department of Commerce, Statistical Abstract of the 
United States 1986, Table No. 808. 


American Gas Association, Rally for Fuel Savings, 1986. 


American Data Association, Typical Questions and Answers 
About Natural Gas Vehicles, 1986. 


ene 


ee 


Gr 


17a 


Ss 


1D" 


ZO. 


Zl 


Ze « 


Zor 


24. 


ZI. 


ZO. 


27]. 


28. 


Davis, Margaret N., "An Examination of the Use of 
Natural Gas Vehicles by Gas Utilities," Gas Energy 
Review, V. 13, N. 5, May 1985. 


American Gas Association, Cost Comparisons of Natural 
Gas Vehicles Versus Gasoline-Fueled Vehicles Under 


Various Refueling Options, 28 February, 1986. 


Telephone interview with Dr. Jeffrey Seisler, American 
Gas Association, Arlington, Virginia, 23 March 1987. 


Department of Defense Instruction 7041.3, Economic 


Analysis and Program Evaluation for Resource Management, 
ikemoOectObelr 1972. 


Blecke, Curtis J., Financial Analysis for Decision 
Making, Prentice-Hall, Inc., 1966. 


Boger, Dan, Presentation at Defense Logistics Agency 
Workshop, "Alternative Vehicle Propulsion and the 
Optimal Industrial Fleet," 6 December 1985. 


Naval Postgraduate School Transportation Office, "1986 
Usage Record," "1986 Budget/Expense Report." 


Interviews with Ensign John Ehlert, Naval Postgraduate 
School Transportation Officer, March 1987. 


Driebeek, Norman J., Applied Linear Programming, 
Addison-Wesley Publishing Co., 1969. 


Lee, S.M., Moore, L.J. and Taylor, B.W., Management 
Science, Wm. C. Brown Publishers, 1981. 


Garfinkel, R.S. and Nemhauser, Gs Ls; Integer 
Programming, John Wiley & Sons, 1972. 


Boger, Dan, "Alternative Vehicle Propulsion and the 
Optimal Industrial Fleet." 


Interviews with Ensign John Ehlert, Naval Postgraduate 
Ecce lransportaction Officer, April 1987. 


Telephone interview with William Kummer, Texaco 


Marketing Representative, Los Angeles, California, 6 May 
oS 7/ . 


72 


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